NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs

  • Sepp Hartung
  • André Nichterlein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)


In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match the given sequence. This realization problem is known to be polynomial-time solvable when the graph is directed or undirected. In contrast, we show NP-completeness for the problem of realizing a given sequence of pairs of positive integers (representing indegrees and outdegrees) with a directed acyclic graph, answering an open question of Berger and Müller-Hannemann [FCT 2011]. Furthermore, we classify the problem as fixed-parameter tractable with respect to the parameter “maximum degree”.


graph realization problems combinatorial algorithms parameterized complexity realizing topological orderings 


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sepp Hartung
    • 1
  • André Nichterlein
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTechnische Universität BerlinBerlinGermany

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